In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several grap...
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize...
Assuming that every proper minor closed class of graphs contains a maximum with respect to the homomorphism order, we prove that such a maximum must be homomorphically equivalent ...